Bar-Natan Homology for null homologous links in \mathbb{RP}^3
Abstract
In this paper, we introduce Bar-Natan homology for null homologous links in \mathbb{RP}^3 over the field of two elements. It is a deformation of the Khovanov homology in \mathbb{RP}^3 defined by Asaeda, Przytycki and Sikora. We also define an s-invariant from this deformation using the same recipe as for links in S^3, and prove some genus bound using it. The key ingredient is the notion of twisted orientation for null homologous links and cobordisms in \mathbb{RP}^3.
- Publication:
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arXiv e-prints
- Pub Date:
- July 2023
- DOI:
- 10.48550/arXiv.2307.11461
- arXiv:
- arXiv:2307.11461
- Bibcode:
- 2023arXiv230711461C
- Keywords:
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- Mathematics - Geometric Topology;
- 57K18
- E-Print:
- 29 pages, 21 figures. Comments are welcome